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strojnjashka [21]
3 years ago
12

Professor Stache awarded 500 certificates, some for math, and some for science. Girls won 2/3 of the math certificates and 1/2 o

f the science certificates. If the number of girls who won for math was 50 more than 3/2 the number of girls who won for science, how many girls won for math?
Mathematics
1 answer:
wariber [46]3 years ago
5 0

Answer:

  • 200

Step-by-step explanation:

<u>Given:</u>

  • Total certificates = 500
  • Math = m
  • Science = s

<u>Equations </u>

  • m+s = 500  ⇒ s = 500 - m

<u>Girls who won certificates:</u>

  • 2/3m = 50 + 3/2*1/2s
  • 2/3m = 50 + 3/4s

<u>Multiply both sides by 12 to clear fractions</u>

  • 8m = 600 + 9s

<u>Substitute s</u>

  • 8m = 600 + 9(500 - m)
  • 8m = 600 + 4500 - 9m
  • 17m = 5100
  • m = 5100/17
  • m =300

<u>Girls who won math:</u>

  • 2/3*300 = 200
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